📐algorithm-groupant-wave26-transforms

The groupant beside algorithms/tests/groupant_wave26_transforms.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.

Facts

Components

Obernants

The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.

Model text

descriptant

Transform composition tests

Prospective integration test model

Before implementation: orthonormal Haar and DCT preserve norm separately; composing DCT(Haar(x)) then inverse DCT then inverse Haar reconstructs x in real arithmetic, provided intermediate vectors stay inside input caps. Independent norm is sum of sample squares. Goertzel requested bins must match same bins of complex Bluestein on zero-imaginary samples; independent negative-phase trigonometric sums prevent shared-sign false agreement. Savitzky-Golay on degree<=d unit-grid polynomials reproduces target values, including shifted windows; independently construct unscaled Vandermonde QR fits and compare predictions and analytic values. Invalid domains must remain tagged errors rather than entering compositions. Finite fixture tolerances only; no universal rounding certificate. Three tests, bounded work; no timing. Compile one production sign mutant in Goertzel, require named spectral composition assertion failure, restore exact source and rerun. Harness twice debug/release with identical normalized outcomes.

Mathematical combiner

Partial syntax binds the test transition. Forward model specifies finite assertions; complement excludes incompatible observations; reconstruction describes implementation fibers. Orthogonal, spectral and smoothing specializations model public wiring. Independent analytic anchors constrain shared-kernel agreement; finite passing observations do not prove semantics. No macro expansion or semantic AST. Underlying algorithm references remain in Haar, DCT, Bluestein, Goertzel and Savitzky-Golay modules.

Observed epoch 2026-10-30

Three tests twice debug and twice release, normalized pass records identical; Goertzel production imaginary-sign mutant compiled and failed selected_spectrum_matches_bluestein_and_direct_dft, restored exact source and all three positives pass. Strict focused Clippy and formatting pass; paired source syntax byte-identical.

Evidence: $MOVA_DATA/runs/octopus-wave26-transforms-2026-10-30. No timing or universal accuracy claim.

model

behavior_complement

Pass excludes any implementation whose fixture observations violate Parseval, inverse reconstruction, independent negative-phase DFT sums, analytic polynomial reproduction, cross-kernel agreement or explicit domain-error tags. It does not exclude untested numerical defects; same-output shared bugs can survive cross-comparison alone, hence independent anchors.

reverse_reconstruction

Pass identifies the equivalence class of implementations satisfying the finite asserted observations within tolerances. Many implementations differ off-grid or outside fixtures and still pass; implementations differing within tolerance can also pass. A failed assertion identifies at least one violated observed relation, not a unique faulty kernel or source repair. Full transform inversion requires all coefficients and second-call domain admissibility; selected bins and local smoothing generally have ambiguous preimages.

orthogonal_composition

Haar and DCT are real orthogonal maps with energy preservation; DCT(Haar(x)) inverse is Haar-inverse(DCT-inverse(y)), reversing order. Fixture amplitudes keep every intermediate in both API domains. Sum-of-squares is independent of transform recurrence; tolerances account for finite rounding.

spectral_composition

Real input embeds as Complex(re=x,im=0). Goertzel's ordered repeated integer bins select Bluestein's negative-forward, unnormalized DFT entries. Independent direct sums for every selected k detect common sign/normalization mistakes; input n includes primes, powers and singleton.

smoothing_composition

Known degree0..4 polynomials at n=17 lie in the seven-point fitting space. Every boundary output is checked against analytic polynomial and independent unscaled target-centered Vandermonde QR. QR comparison alone is shared dependency, so analytic values remain authoritative anchor.

oracle_independence

Energy sums, trigonometric direct DFT and analytic polynomial values do not call production kernels to construct expected results. QR is a supplementary composition comparison, not the sole oracle.

mutation_sensitivity

Negating Goertzel terminal imaginary component compiles and fails named spectral composition assertion; unchanged original bytes are restored before all-three positive rerun. Compile failure alone does not count as detection.

finite_scope

Finite deterministic fixture/tolerance coverage is not all-f64 verification, a performance claim or a 1/2/5/10% surrogate certificate. Allocation exhaustion is not injected; callbacks are absent. Independent oracle formulas also round in f64.

approximant

Forward and invariant

Three integration tests run public APIs on bounded finite fixtures: orthogonal_composition_parseval_and_roundtrip checks individual Haar/DCT Parseval and DCT(Haar(x)) inversion; selected_spectrum_matches_bluestein_and_direct_dft checks requested Goertzel bins against Bluestein and independent negative-phase DFT sums; smoothing_matches_polynomials_and_unscaled_qr checks shifted-window smoothing against known polynomial values and independently formed unscaled QR. Invalid input assertions preserve distinct empty/shape/value policies.

Every successful test terminates without assertion panic and validates both independent expected values and composition wiring. Input data are immutable; errors must match explicit tags. O(sum n²) for DCT/direct DFT plus bounded local QR work, finite vectors up to 128 samples. Allocation policy inherits production and standard test allocations. No callback cost. Floating agreement uses absolute tolerance 2e-8*(1+abs(reference)), defining finite-observation neighborhoods, not a universal relative bound. Inverse laws depend on second-call magnitude caps.

tests

Three tests twice debug and twice release, normalized pass records identical; Goertzel production imaginary-sign mutant compiled and failed selected_spectrum_matches_bluestein_and_direct_dft, restored exact source and all three positives pass. Strict focused Clippy and formatting pass; paired source syntax byte-identical.

Empty-domain differences, nondyadic lengths, bin-range errors, NaN/infinity, invalid smoothing window and underdetermined QR are asserted. No resource fault injection.

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